How Do You Solve a Physics Problem Involving Two Masses and a Pulley?

[joemama69]

Homework Statement

An unknown mass, m1, hangs from a massless string and descends with an acceleration g/2. The other end is attached to a mass m2 which slides on a frictionless horizontal table. The string goes over a uniform cylinder of mass m2/2 and radius R. The cylinder rotates about a horizontal axis without friction and the string does not slip on the cylinder. Express your answers in parts b, c, and d in terms of g, m2 and R.

a) Draw free-body diagrams for the cylinder and the two masses.

b) What is the tension in the horizontal section of the string?

c) What is the tension in the vertical section of the string?

d) What is the value of the unknown mass m1?

Homework Equations

The Attempt at a Solution

part b)

T<sub>1/SUB] = m2/SUB]a
T2/SUB] -m1/SUB]g = -m1/SUB]a
T2/SUB]R - T1/SUB]R = MR<sup>2/SUP]$$\alpha$$...T2/SUB] - T1/SUB] = Ma

T1/SUB] = T2/SUB] - Ma = m1/SUB]g - .5m1/SUB]g - .25m2/SUB]g = g(.5m1/SUB] - .25m2/SUB])

part c)

T2/SUB] = T1/SUB] + Ma = .5m2/SUB]g + .25m2/SUB]g = .75m2/SUB]g

part d) it keeps canceling out,, is something wrong above</sup></sub>

 

[Nate810]

?m_{1/SUB] = (T2/SUB] - T1/SUB])/(g/2) = (.75m2/SUB] - (g(.5m1/SUB] - .25m2/SUB]))/(g/2)}

 

[kerimek]

?


I would first commend the student for their attempt at solving the problem and using the appropriate equations. However, it seems that there may be some errors in their calculations. I would suggest going back and carefully checking each step to ensure accuracy. Additionally, it may be helpful to draw a free-body diagram for each mass and the cylinder to better visualize the forces at play. Once the equations are correctly set up, solving for the unknown mass m1 should be possible.